In other words, we believe that every permutation is almost entirely filled by a square.
Notice that a repeated application of the Erdős-Szekeres Theorem ([1]}) implies that every \(n\) -permutation contains an \(\Omega (\sqrt{n})\) -square. Clearly, the components of this square are monotone. It is, therefore, natural to expect even larger squares with components of an arbitrary pattern.
